The primary impediment to formulating a general theory for adaptive evolution has been the unknown distribution of fitness effects for new beneficial mutations. By applying extreme value theory, Gillespie (1984) circumvented this issue in his mutational landscape model for the adaptation of DNA sequences and Orr (2002) extended Gillespie's model, generating testable predictions regarding the course of adaptive evolution. Rokyta et.al. (2005) provided the first empirical examination of this model, using an ssDNA bacteriophage.
Now that we can begin to test aspects of the theory based on empirically generated data, a number of interesting statistical issues arise. In this talk several statistical procedures to test both the assumptions and predictions of the Gillespie-Orr model are presented. I will outline these procedures and give some guidance as to how much data should be collected and compare the power of our procedures versus more commonly used statistical tests.
In the end the Rokyta data is reanalyzed in light of the new methodology. Several of the underlying assumptions of the Gillespie-Orr model are shown to be violated, but many of the general conclusions of the model are robust with respect to these violations.